Solitons
introduction
- Solitons were discovered experimentally (Russell 1844)
- analytically (Korteweg & de Vries, 1895)
- modelling of Russell's discovery
- 1-soliton solution
- numerically (Zabusky & Kruskal 1965).
- interaction of two 1-soliton solutions
- they discovered that solitons of differenct sizes interact cleanly
meaning of soliton
- "soliton" is used to describe their particle-like properties like bosons, fermions and hadrons
- any localized nonlinear wave which interacts with another (arbitrary) local disturbance and always regains asymptotically its exact initial shape and velocity (allowing for a possible phase shift)
PDEs
important techniques
history
하위페이지
- soliton
- Boussinesq equation
- course design on soliton
- Fermi-Pasta-Ulam problem
- Frenkel-Kontorova dislocation
- Hamiltonian structure
- Kadometsev-Petviashvii equation (KP equation)
- KdV equation
- methods and theory
- Nonlinear Schrodinger equation
- quantum sine-Gordon field theory
- restricted sine-Gordon theory
- sine-Gordon equation
- Boussinesq equation
computational resource
- KdV equation
- sine-Gordon equation[[5398019/attachments/3290825|]]
- [1]http://physics.ucsc.edu/~peter/250/mathematica/
books
- Integrable Models (World Scientific Lecture Notes in Physics)Ashok Das
- Soliton, Toda
- Theory of Nonlinear Lattices, Morikazu Toda
- Nonlinear evolution equations solvable by the spectral transform, Eds. Calogero, 1977
- Solitons and Nonlinear Wave Equations, R.K.Dodd, J.C.Eilbeck, J.D.Gibbon, H.C.Morries, Academic Press, London, 1982
- 2010년 books and articles
- http://gigapedia.info/1/soliton
- http://gigapedia.info/1/
- http://gigapedia.info/1/
- http://gigapedia.info/1/
- http://www.amazon.com/s/ref=nb_ss_gw?url=search-alias%3Dstripbooks&field-keywords=
encyclopedia
- http://ko.wikipedia.org/wiki/
- http://en.wikipedia.org/wiki/Soliton
- http://en.wikipedia.org/wiki/
- http://en.wikipedia.org/wiki/
- http://en.wikipedia.org/wiki/
- Princeton companion to mathematics(Companion_to_Mathematics.pdf)
expositions
- Why are solitons stable? Terence Tao, 2008[2]
- An Introduction to Wave Equations and Solitons Richard S. Palais
- Richard S Palais, “The Symmetries of Solitons,” dg-ga/9708004 (August 8, 1997), http://arxiv.org/abs/dg-ga/9708004. [3]http://dx.doi.org/10.1090/S0273-0979-97-00732-5
- Ford, Joseph. 1992. The Fermi-Pasta-Ulam problem: Paradox turns discovery. Physics Reports 213, no. 5 (May): 271-310. doi:10.1016/0370-1573(92)90116-H.
- A brief history of the quantum soliton with new results on the quantization of the Toda lattice Bill Sutherland, Rocky Mountain J. Math. Volume 8, Number 1-2 (1978), 413-430.
articles
- Solitons, Links and KnotsRichard Battye, Paul Sutcliffe, Proc. R. Soc. Lond. A 8 December 1999 vol. 455 no. 1992 4305-4331
- The Symmetries of SolitonsRichard S. Palais, Journal: Bull. Amer. Math. Soc. 34 (1997), 339-403
- From Solitons to Knots and Links Miki Wadati and Yasuhiro Akutsu, Prog. Theor. Phys. Supplement No.94 (1988) pp. 1-41
- Lax, P. D. 1996. Outline of a Theory of the KdV Equation in Recent Mathematical Methods in Nonlinear Wave Propagation. Lecture Notes in Mathematics, volume 1640, pp. 70–102. New York: Springer.
- Russell, J. S. 1844. Report on waves. In Report of the 14th Meeting of the British Association for the Advancement of Science, pp. 311–90. London: John Murray.
- Toda, M. 1989. Nonlinear Waves and Solitons. Dordrecht: Kluwer.
- Zabusky, N. J., and M. D. Kruskal. 1965. Interaction of solitons in a collisionless plasma and the recurrence of initial states. Physics Review Letters 15:240–43.
question and answers(Math Overflow)
blogs
experts on the field